The paper helps to understand the essence of stochastic population-based searches that solve ill-conditioned global optimization problems. This condition manifests itself by presence of lowlands, i.e., connected subsets of minimizers of positive measure, and inability to regularize the problem. We show a convenient way to analyze such search strategies as dynamic systems that transform the sampling measure. We can draw informative conclusions for a class of strategies with a focusing heuristic. For this class we can evaluate the amount of information about the problem that can be gathered and suggest ways to verify stopping conditions. Next, we show the Hierarchic Memetic Strategy coupled with Multi-Winner Evolutionary Algorithm (HMS/MWEA) that follow the ideas from the first part of the paper. We introduce a complex, ergodic Markov chain of their dynamics and prove an asymptotic guarantee of success. Finally, we present numerical solutions to ill-conditioned problems: two benchmarks and a real-life engineering one, which show the strategy in action. The paper recalls and synthesizes some results already published by authors, drawing new qualitative conclusions. The totally new parts are Markov chain models of the HMS structure of demes and of the MWEA component, as well as the theorem of their ergodicity.

本文有助于理解基于随机种群的搜索的本质，该搜索解决了条件不佳的全局优化问题。这种情况表现为低地的存在，即积极措施的最小化部分的相连子集，并且无法解决问题。我们展示了一种方便的方法来分析诸如转换抽样方式的动态系统之类的搜索策略。我们可以针对具有启发式重点的一类策略得出有益的结论。对于此类，我们可以评估可以收集的有关问题的信息量，并提供验证停止条件的方法。接下来，我们将遵循分层模因策略以及多赢者进化算法（HMS / MWEA），该策略遵循本文第一部分的思想。我们介绍一个复杂的 遍历马尔可夫链的动力学，证明了成功的渐近保证。最后，我们提出了病态问题的数值解决方案：两个基准和一个现实生活中的工程基准，它们显示了实际的策略。该论文回顾并综合了作者已经发表的一些结果，得出了新的定性结论。全新的部分是马尔科夫链模型，这些模型具有Demes的HMS结构和MWEA组件，以及它们的遍历性定理。